When President Obama was locked in painful spending negotiations with House Republicans last spring, his exceedingly meticulous budget director, Jacob J. Lew, went to the Oval Office to propose some complex budget changes.

As Mr. Lew delved deeper and deeper into the numbers, Mr. Obama put up his hand, signaling him to stop.

Today Mr. Lew is the White House chief of staff (and on the shortlist to become the next Treasury secretary), and Mr. Obama has entrusted him with an even bigger task: guiding the White House through potentially treacherous negotiations with Congressional Republicans to avert automatic tax increases and spending cuts on Jan. 1, which economists warn could throw the country back into recession.

An agreement by year's end could lead to a long-term deficit reduction plan, helping Mr. Obama live up to his promise to bring both parties together and sealing Mr. Lew's reputation as the master of the Washington budget deal. But if the talks fail, Mr. Obama might be remembered as the president who could not break partisan gridlock in Washington, and Mr. Lew could wind up with a blot on his nearly impeccable record.

"This is a reset moment for the administration and for Jack," said Tom Daschle, a former Senate Democratic leader. "It's a window that will close in a few weeks, but it really is an opportunity to start over. Part of the message of the election was 'You guys have got to work together.' "

But Mr. Lew's last go-round with Republicans, the debt ceiling talks in the summer of 2011, ended uncharacteristically badly. Mr. Lew, still the budget director at the time, irked Speaker John A. Boehner and his staff, who viewed him as an uncompromising know-it-all. Mr. Lew's defenders call it an aberration.

"I think it's because Jack knows the numbers, and they couldn't pull a fast one," said David Plouffe, Mr. Obama's chief political adviser.

This time, Treasury Secretary Timothy F. Geithner is the lead negotiator; as the chief of staff, administration officials say, Mr. Lew can no longer spend long hours away from the White House. Instead, he is overseeing the talks and plotting strategy from his West Wing office, where a painting of Abraham Lincoln hangs over the fireplace and a tiny ceramic replica of Ellis Island — a nod to his father, who immigrated from Poland — sits on his orderly wooden desk.

So far, there has been little progress. On Friday, Mr. Boehner declared the talks "at a stalemate," while Mr. Obama hit the road to sell his plan to raise taxes on income over $250,000. Earlier in the week, Mr. Obama met with business leaders, as did Mr. Lew, who declined to comment for this article.

At 57, Mr. Lew may be the most unassuming power broker in Washington. He is deeply religious (an Orthodox Jew, he leaves work each Friday before sundown) and is so strait-laced that his colleagues feel compelled to apologize when they curse in front of him. He brings his own lunch (a cheese sandwich and an apple) and eats at his desk.

With his owlish glasses and low-key manner, Mr. Lew may come off as just a policy nerd. But he is a fierce negotiator. When defending social safety net programs, particularly those like Medicaid that help the poor, he morphs into a warrior, Republicans say, though he has proved willing to make concessions.

"Jack is tough," said Jim Dyer, a Republican and a former Capitol Hill aide who negotiated budget issues with Mr. Lew in the 1990s. "He can be argumentative, he's smart as hell, he's very political, he is a true liberal, he is loyal to his superiors, and he has a good grasp of budgetary and policy issues."

"Fighting with him is exhausting," Mr. Dyer added. "We yelled at each other a lot. We never came to blows. We walked away from the table perhaps happy to be away from each other for a while, but perhaps equally happy that we preserved a modicum of what each side wanted."

Mr. Lew arrived in Washington in 1973, a skinny, bookish 18-year-old from Queens who got his first taste of Democratic politics at 12 while handing out fliers for Eugene McCarthy's presidential campaign. Today, as a two-time former budget director (he also held the job under President Bill Clinton), he has an intricate understanding of budget policy.

In 1983, as an aide to Speaker Tip O'Neill when Ronald Reagan was president, Mr. Lew helped put Social Security on a path to solvency with a plan that, to many Democrats' chagrin, will eventually raise the retirement age to 67. He keeps a gavel from the day the legislation passed, signed by Mr. O'Neill, on a bookshelf in his office.

In 1997, under Mr. Clinton, Mr. Lew worked with Republicans to balance the federal budget, enabling the president to leave office with a surplus.

Mr. Lew also has foreign policy experience; he spent the first two years of the Obama administration as a deputy to Secretary of State Hillary Rodham Clinton.

He has little use for Washington's social scene; a check of newspaper archives going back to 1977 shows that Mr. Lew has never turned up in The Washington Post's gossip column. His wife, Ruth, lives in their home in the affluent Riverdale section of the Bronx; they commute back and forth and have a daughter in Washington and a son in New York. He likes to cook; he makes a pretty good chicken soup (Ruth is in charge of the matzo balls) and a mean potato kugel.

Mr. Lew's worldview was forged in the late 1960s and early 1970s in Forest Hills, Queens, where he grew up in the middle class in a squat brick apartment building in a neighborhood of bagel shops and corner luncheonettes. His father practiced law solo and dealt in rare books; his mother managed his father's office. In high school, Mr. Lew found himself in music (he played the 12-string guitar), edited the newspaper and fought for causes like building low-income housing in Queens.

"Jack was a folkie," said an old friend, Stephen Norman. As a teenager, Mr. Lew liked to hang around the now-defunct Folklore Center in Greenwich Village, where he ran into Don McLean, who had not yet written "American Pie." When the young Mr. Lew organized a fund-raiser to fight world hunger, he persuaded Mr. McLean to play.

If he had a teenage rebellion, it was moving to Minnesota to attend Carleton College (his parents preferred Columbia University) and then quitting after a year to work for Bella Abzug, the flamboyant Manhattan congresswoman. His mother worried that he would never get his degree, but he did, at Harvard. Later, while working on Capitol Hill, he picked up a law degree, attending Georgetown at night.

By the time he was 23, Mr. Lew was a top policy aide to Mr. O'Neill, an experience that friends say sharpened his sense of how federal spending affects people's lives.

"When he said 'Pell grants,' it wasn't something distant or numerical," said Chris Matthews of MSNBC, who also worked for Mr. O'Neill and shared an office with Mr. Lew. "He knew this meant kids could go to college who didn't have rich parents."

The challenge now for Mr. Lew — and for Mr. Obama — is to forge an agreement that does not cut too deeply into the entitlement programs that Democrats cherish. Like Mr. Obama, Mr. Lew is a pragmatist; one person familiar with his thinking said he had previously expressed willingness to raise the Medicare eligibility age from 65 to 67, a move that many liberals oppose.

If Mr. Lew gets the Treasury job, the business world will not be unhappy. He is not a creature of Wall Street, but before joining the Obama administration, he spent three years in high-level (and high-paying) jobs at Citigroup, where he oversaw a unit that lost money but also profited from betting against the subprime mortgage market. Mr. Lew was chief operating officer; in testimony before Congress, he has said he did not make investment decisions.

For Mr. Obama, the choice is whether he needs Mr. Lew more in overseeing the Treasury Department or in running the White House. Though Mr. Lew, who has been the chief of staff for less than a year, is not a member of Mr. Obama's longtime Chicago inner circle, aides say he is a good fit — "the no-drama chief of staff for the no-drama president," one said — and Mr. Obama relies on him for more than just budget advice.

have been in countless meetings with the president and Jack," said Valerie Jarrett, Mr. Obama's senior adviser, "and also been in meetings with senior staff where Jack hasn't been present, where the president will say, 'What does Jack think?'"